Hi Bojan Andonovski,
I see that you want to implement Shrinking-Circle Method Based on Time Difference of Arrival (TDoA) in MATLAB. The approach you are referring to is an iterative method for source localization using Time Difference of Arrival (TDoA) measurements. The shrinking-circle method refines the estimated position of the source by iteratively adjusting the radius of a circle centred on a receiver until the circle passes through the source.
To implement this in MATLAB, you will need to establish a few things:
- TDoA Measurements: The time differences of arrival at various receivers from the source.
- Receiver Positions: The known positions of the receivers.
- Initial Estimates: Initial estimates for Rmax and Rmin. These could be based on the maximum possible distance in your environment and a minimum distance that is greater than zero, respectively.
Here is a sample code for the same:
function [X] = shrinking_circle(TDoA, receiver_positions, initial_Rmax, initial_Rmin, TH1, TH2)
% TDoA: Time Difference of Arrival measurements
% receiver_positions: Known positions of receivers
% initial_Rmax: Initial maximum radius estimate
% initial_Rmin: Initial minimum radius estimate
% TH1: Threshold for the function f(r1)
% TH2: Threshold for the difference between Rmax and Rmin
% Step 1: Initialize Rmax and Rmin
Rmax = initial_Rmax;
Rmin = initial_Rmin;
% Start the iteration process
while true
% Step 2: Compute Rmid
Rmid = (Rmax + Rmin) / 2;
% Step 3: Calculate the solution X when r1 equals Rmid
% This involves solving the equations based on TDoA measurements
% and the known positions of the receivers.
X = calculate_position(TDoA, receiver_positions, Rmid);
f_r1 = calculate_f_r1(X, TDoA, receiver_positions);
% Step 4: Update Rmax and Rmin
if f_r1 > 0
Rmin = Rmid;
else
Rmax = Rmid;
end
% Step 5: Check termination conditions
if abs(f_r1) < TH1 || abs(Rmax - Rmin) < TH2
break;
end
end
% The final position of the target
end
function X = calculate_position(TDoA, receiver_positions, Rmid)
% Implement the position calculation using TDoA and Rmid
% This typically involves solving a set of nonlinear equations
% which can be done using optimization techniques or algebraic methods.
% Placeholder for actual implementation:
X = [0, 0]; % Replace with actual calculation
end
function f_r1 = calculate_f_r1(X, TDoA, receiver_positions)
% Implement the calculation of the function f(r1) based on the
% estimated position X, TDoA measurements, and receiver positions.
% Placeholder for actual implementation:
f_r1 = 0; % Replace with actual calculation
end
In the above code, “calculate_position” and “calculate_f_r1” are placeholder functions where you would implement the specific calculations required to determine the source position X and the evaluation of the function f(r1) based on the TDoA measurements and receiver positions.
I hope this helps!
Best Regards,
Abhishek Chakram
